A332121 a(n) = 2*(10^(2n+1)-1)/9 - 10^n.

1, 212, 22122, 2221222, 222212222, 22222122222, 2222221222222, 222222212222222, 22222222122222222, 2222222221222222222, 222222222212222222222, 22222222222122222222222, 2222222222221222222222222, 222222222222212222222222222, 22222222222222122222222222222, 2222222222222221222222222222222

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

a(n) = 2*A138148(n) + 1*10^n = A002276(2n+1) - 10^n.

G.f.: (1 + 101*x - 300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

Maple

A332121 := n -> 2*(10^(2*n+1)-1)/9-10^n;

Mathematica

Array[2 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]

Prog

(PARI) apply( {A332121(n)=10^(n*2+1)\9*2-10^n}, [0..15])
(Python) def A332121(n): return 10**(n*2+1)//9*2-10**n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

Cf. A332131 .. A332191 (variants with different repeated digit 3, ..., 9).

Sequence in context: A344423 A238023 A204299 * A083962 A007942 A210257

Adjacent sequences: A332118 A332119 A332120 * A332122 A332123 A332124

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved